Answer
$-4(4x-1)^{-2} $
Work Step by Step
We have: $f(x)=(4x-1)^{-1}$
We differentiate both sides with respect to $x$.
$f^{\prime}(x)=\dfrac{d}{dx} [(4x-1)^{-1}] \\=(-1) (4x-1)^{-1-1}\dfrac{d}{dx}(4x-1)\\=-4(4x-1)^{-2} $
Simplify to obtain:
$f^{\prime}(x)=-4(4x-1)^{-2} $
